Why does my UI look different
These are two completely different versions of Blender.

You are using 2.79, the current stable official version, the tutorial you are following is for the upcoming 2.8 version, a major refactor of the application, currently in release candidate phase.

You can download both from the Build Bot, but have in mind that 2.8 is not ready yet and is not advised for production. While backwards compatible, both versions are also considerably different, so it is unadvised to switch between the two with the same project.